## Precise control of broadband frequency chirps using optoelectronic feedback

Optics Express, Vol. 17, Issue 18, pp. 15991-15999 (2009)

http://dx.doi.org/10.1364/OE.17.015991

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### Abstract

We demonstrate the generation of wideband frequency sweeps using a semiconductor laser in an optoelectronic feedback loop. The rate and shape of the optical frequency sweep is locked to and determined by the frequency of a reference electronic signal, leading to an agile, high coherence swept-frequency source for laser ranging and 3-D imaging applications. Using a reference signal of constant frequency, a transform-limited linear sweep of 100 GHz in 1 ms is achieved, and real-time ranging with a spatial resolution of 1.5 mm is demonstrated. Further, arbitrary frequency sweeps can be achieved by tuning the frequency of the input electronic signal. Broadband quadratic and exponential optical frequency sweeps are demonstrated using this technique.

© 2009 OSA

## 1. Introduction

1. M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. **40**(1), 10–19 (2001). [CrossRef]

2. J. Zheng, “Analysis of Optical Frequency-Modulated Continuous-Wave Interference,” Appl. Opt. **43**(21), 4189–4198 (2004). [CrossRef] [PubMed]

*δz*of an FMCW range measurement is determined by the total frequency excursion

*B*of the optical source [3]where

*c*is the speed of light. The key component of an FMCW imaging system is therefore a broadband and precisely controllable swept frequency source. The wide gain bandwidth of the semiconductor quantum well media, the narrow linewidth of a single mode semiconductor laser (SCL), and the ability to electronically control the lasing frequency using the injection current make the SCL an attractive candidate for a wideband swept-frequency source for FMCW imaging [4

4. G. Beheim and K. Fritsch, “Remote displacement measurements using a laser diode,” Electron. Lett. **21**(3), 93–94 (1985). [CrossRef]

7. E. M. Strzelecki, D. A. Cohen, and L. Coldren, “Investigation of tunable single frequency diode lasers for sensor applications,” J. Lightwave Technol. **6**(10), 1610–1618 (1988). [CrossRef]

8. K. Iiyama, L.-T. Wang, and K. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. **14**(2), 173–178 (1996). [CrossRef]

## 2. System description

*τ*, and is incident on a photodetector (PD). When the optical frequency is varied with time, the frequency of the generated photocurrent is proportional to the slope of the optical frequency chirp. The output of the PD is mixed down using a reference signal of frequency

*ω*, integrated and is injected into the SCL. Since the injection current into the SCL also modulates the optical power, a low-speed amplitude controller is used to maintain a constant output power. An offset voltage added to the integrator input is used to set the nominal optical frequency slope, and to provide an open-loop pre-distortion as described in Section 2.2.

_{R}*ξ*is the slope of the optical frequency sweep. This corresponds to an optical phase

*K*is the product of the optical power and the PD responsivity, and we have ignored the DC term in the PD output. Equation (4) describes a sinusoidally varying photocurrent with frequency

_{P}*ω*. The mixer output is thenwhere

_{PD}= ξτ*K*is the mixer gain. Let the frequency of the reference oscillator be chosen so that

_{M}*i*vs.

*t*current to the laser, which in turn produces a frequency output as given by Eq. (2), thus providing a self-consistent solution.

*τ*, 0]. If the MZI delay

*τ*is chosen sufficiently small so that the effect of higher order derivatives of the optical frequency can be neglected, Eq. (8) reduces tothe solution to which is a linear frequency chirp as given by Eq. (2).

*ω*as given by Eq. (6), and can be varied by using a VCO for the reference signal. The loop integrator is reset at the desired pulse repetition frequency (PRF) of the output chirped waveform.

_{R}### 2.1 Small signal analysis

*K*denotes the total DC loop gain, given by the product of the gains of the laser, PD, mixer and the integrator. The phase noise of the laser and the phase excursion due to the non-linearity of the frequency-vs.-current response of the SCL are lumped together and denoted by

*τ*is the loop propagation delay. The non-linearity and laser phase noise within the loop bandwidth are suppressed by the loop, as seen from the first term in Eq. (10). The frequency components of the non-linearity are of the order of the repetition frequency of the waveform, and are therefore suppressed by the loop. The reduction in the phase noise of the SCL improves its coherence, leading to a higher signal-to-noise ratio in an FMCW interferometric experiment [10

_{d}10. N. Satyan, W. Liang, and A. Yariv, “Coherence cloning using semiconductor laser optical phase-lock loops,” IEEE J. Quantum Electron. **45**(7), 755–761 (2009). [CrossRef]

### 2.2 Pre-distortion of the SCL input current

*di/dt*. The resultant PD frequency

*ω*is measured, and the distortion function

_{PD}(t)*F*is extracted. This function is then used to solve Eq. (12) numerically, to obtain the pre-distortion current

_{dist}(i)*i*that results in the desired

_{pre}(t)*ω*. The predistortion of the input current significantly reduces the non-linearity and enables phase-locking over a large frequency range, as seen in Section 3.1.

_{PD}(t)## 3. Experimental demonstration

^{14}Hz/s, or a frequency excursion of 100 GHz in the designed pulse repetition period of 1 ms.

### 3.1 Linear frequency sweep

### 3.2 Range resolution measurement

### 3.3 Arbitrary frequency sweeps

*ω*is varied with time, the optical frequency is given bywhere we have used Eq. (9) to relate the slope of the optical frequency to the reference frequency. This principle was experimentally demonstrated by the generation of quadratic and exponential optical frequency sweeps as shown in Figs. 8(a) and 8(b) respectively. In the former case, the reference frequency was varied linearly between 1.43 MHz and 4.29 MHz over 1 ms. This corresponds to a linear variation of the optical frequency slope from 50 GHz/ms to 150 GHz/ms, and consequently, a quadratic variation of the optical frequency. In the latter case, the reference frequency was varied exponentially between 4.29 MHz and 1.43 MHz according to the relation

_{R}(t)## 4. Summary

^{16}Hz/s are achievable using this technique.

## Acknowledgement

## References and links

1. | M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. |

2. | J. Zheng, “Analysis of Optical Frequency-Modulated Continuous-Wave Interference,” Appl. Opt. |

3. | W. S. Burdic, |

4. | G. Beheim and K. Fritsch, “Remote displacement measurements using a laser diode,” Electron. Lett. |

5. | E. C. Burrows and K.-Y. Liou, “High-resolution laser LIDAR utilizing two-section distributed feedback semiconductor laser as a coherent source,” Electron. Lett. |

6. | A. Dieckmann, “FMCW-LIDAR with tunable twin-guide laser diode,” Electron. Lett. |

7. | E. M. Strzelecki, D. A. Cohen, and L. Coldren, “Investigation of tunable single frequency diode lasers for sensor applications,” J. Lightwave Technol. |

8. | K. Iiyama, L.-T. Wang, and K. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. |

9. | F. M. Gardner, |

10. | N. Satyan, W. Liang, and A. Yariv, “Coherence cloning using semiconductor laser optical phase-lock loops,” IEEE J. Quantum Electron. |

11. | I. V. Komarov, and S. M. Smolskiy, |

**OCIS Codes**

(140.3490) Lasers and laser optics : Lasers, distributed-feedback

(280.3640) Remote sensing and sensors : Lidar

(140.3518) Lasers and laser optics : Lasers, frequency modulated

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: April 23, 2009

Revised Manuscript: August 14, 2009

Manuscript Accepted: August 19, 2009

Published: August 25, 2009

**Citation**

Naresh Satyan, Arseny Vasilyev, George Rakuljic, Victor Leyva, and Amnon Yariv, "Precise control of broadband frequency chirps using optoelectronic feedback," Opt. Express **17**, 15991-15999 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-18-15991

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### References

- M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001). [CrossRef]
- J. Zheng, “Analysis of Optical Frequency-Modulated Continuous-Wave Interference,” Appl. Opt. 43(21), 4189–4198 (2004). [CrossRef] [PubMed]
- W. S. Burdic, Radar signal analysis (Prentice-Hall, 1968), Chap. 5.
- G. Beheim and K. Fritsch, “Remote displacement measurements using a laser diode,” Electron. Lett. 21(3), 93–94 (1985). [CrossRef]
- E. C. Burrows and K.-Y. Liou, “High-resolution laser LIDAR utilizing two-section distributed feedback semiconductor laser as a coherent source,” Electron. Lett. 26(9), 577–579 (1990). [CrossRef]
- A. Dieckmann, “FMCW-LIDAR with tunable twin-guide laser diode,” Electron. Lett. 30(4), 308–309 (1994). [CrossRef]
- E. M. Strzelecki, D. A. Cohen, and L. Coldren, “Investigation of tunable single frequency diode lasers for sensor applications,” J. Lightwave Technol. 6(10), 1610–1618 (1988). [CrossRef]
- K. Iiyama, L.-T. Wang, and K. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996). [CrossRef]
- F. M. Gardner, Phaselock Techniques (Wiley 2005).
- N. Satyan, W. Liang, and A. Yariv, “Coherence cloning using semiconductor laser optical phase-lock loops,” IEEE J. Quantum Electron. 45(7), 755–761 (2009). [CrossRef]
- I. V. Komarov and S. M. Smolskiy, Fundamentals of short-range FM radar (Artech House, 2003), Chap. 5.

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